The performance and reliability of semiconductor electronic and optoelectronic devices, and the integrated circuits into which they are incorporated, depends upon the purity of the semiconductor from which the devices are made, and, in particular, on the level of heavy metal contaminants (e.g., Fe, Cr) which may be introduced during manufacture and processing. One measure of contamination that is used in quality control is the minority carrier diffusion length. This parameter is the effective distance that excess carriers diffuse through a semiconductor during their lifetime. The diffusion length gives a measure of the contaminant concentration because heavy metals are recombination centers which reduce carrier lifetime.
In the most common techniques for measuring diffusion length, light is directed by a probe onto a semiconductor to create a surface photovoltage which is detected and analyzed. The photovoltage is created when the energy of the incident photons is above the semiconductor band gap so that excess carriers (holes and electrons) are produced. As a result of the photogeneration and diffusion processes, electron-hole pairs reach the region near the surface and become separated by the electric field of the surface-space charge region, thus producing the surface photovoltage. The photovoltage is typically detected by an electrode that is placed close to the semiconductor surface. The electrode is typically made of a conducting transparent material so that the light which produces the excess carriers can be passed through it.
The American Society for Testing and Materials (ASTM) recommends two methods for analyzing photovoltage to determine diffusion length. In both of these methods, the diffusion length calculation is based on an equation for excess minority carrier concentration at the surface which assumes that the diffusion length is short compared to wafer thickness and that the light penetration depth is less than or equal to one-third the wafer thickness. This expression is: ##EQU1## where .DELTA.n is the excess minority carrier concentration, L is the diffusion length, .alpha. is the absorption coefficient (.alpha..sup.-1 is the penetration depth), .PHI. is the incident photon flux, R is the reflectivity of the semiconductor, D is the minority carrier diffusion constant, D=kT/q.mu., where k is Boltzman's constant, T is the temperature, q is the elemental charge, .mu. is the minority carrier mobility, and S is the surface recombination velocity on the front surface of the semiconductor. This expression is derived in Moss, J. Electronics and Control, 1, 126, (1955).
In the constant magnitude method, one of the ASTM-recommended methods, the relationship between carrier concentration and the photovoltage is assumed to be a monotonic function. For several different wavelengths of light, the photovoltage signal is adjusted to a constant value by adjusting the photon flux. The method assumes that the carrier concentration is constant because the photovoltage is constant. The diffusion length is then obtained, using Equation (1), from a plot of the photon flux, .PHI., as a function of the light penetration depth .alpha..sup.-1, where the diffusion length is the intercept value, L=-.alpha..sup.-1.sub.int at .PHI.=0. The constant magnitude method is further discussed, for example, in Goodman J. Appl. Phys. Vol. 33, p. 2750, 1961, ANSI/ASTM F-391-78, p. 770, 1976, and U.S. Pat. No. 4,337,051.
The second ASTM-recommended method, the linear constant photon flux, relies on measurement for several different wavelengths of light at a very low intensity where the photovoltage is a linear function of the photon flux and where parameters on the right side of the equation (1) are substantially constant. Under such conditions, photovoltage is directly proportional to carrier concentration, or V=const(.DELTA.n), where the constant depends on the semiconductor doping and the surface charge, but does not depend on the photon flux. The effective photon flux entering a semiconductor, .PHI..sub.eff =.PHI.(1-R), is constant for all wavelengths and, thus, for all penetration depths, .alpha..sup.-1. The diffusion length is obtained by plotting the inverse of the photovoltage signal, .PHI..sub.eff /V, as a function of penetration depths, .alpha..sup.-1, and diffusion length is obtained as an intercept value, L=.alpha..sup.-1.sub.int at .PHI..sub.eff /V=0. This method is further discussed in patents to Lagowski, U.S. Pat. No. 5,025,145 and U.S. Pat. No. 5,177,351 and in L. Jastrzebski et al., Solid State Technol. 35, 27 (1992)) and J. Lagowski et al., Semicond. Sci. Technol. 7, A185 (1992).
These techniques have proven satisfactory for many analyses in which the diffusion length is short compared to wafer thickness.